Resurrection: Dragoons, Hussars, & Cuirassier Oh My!
OK, I'll throw something contrarian into this discussion.
What the met thinks on the subject
Since the first firearms appear to have been in use in Europe as early as the third decade of the fourteenth century, and the gradual decline of armor is not noticed before the second half of the seventeenth century, firearms and plate armor coexisted for more than 300 years. During the sixteenth century, attempts had been made to render armor bulletproof, either by hardening the steel or, more commonly, by thickening the armor or adding separate reinforcing pieces on top of the normal field armor.
Finally, it should be noted that armor as such has never become entirely obsolete. The ubiquity of helmets worn by today's soldiers and police forces are proof that armor, although of different materials and having perhaps lost some of its earlier importance, is still an essential part of martial equipment around the world. Moreover, even body defenses have lived on in the shape of the experimental breastplates of the American Civil War, the breastplates of airplane gunners during World War II, and the bulletproof vests worn today.
1700s-1800s
Breastplate & Helmet
I recall, when reading about the battle of Waterloo, that Napoleon had a unit of "Curiassers." There were cavalry armed with light lances & sabres and equipped with a heavy breastplate and helmet. The breastplate was kept as a defense against musket balls, I do believe. These were heavy shock cavalry.
Russian Cuirassier
www.xenophongi.org
French Back & Breast & Helmet (actually mid-late 1600s):
www.3rdcuirassiers.org
1600s
3/4 Plate
Heavy cavalry doffed some of the armor on the lower extremities, but beefed up the breastplate & remaining armor.
Italian 3/4 Plate Manuf between 1610-1620 (note the dent "proof mark")
www.metmuseum.org
In response to the change in weaponry, the armorer increased the thickness of the plate and added reinforces. Our example retains two reinforces, one for the back of the helmet and another covering the breastplate, and it formerly possessed a third as well, for the visor front, rendering it one of the heaviest field armors known. In order to test armors, bullets were fired at them, with the resulting dents left as a guarantee of strength; the breastplate, backplate, and two reinforces exhibit these "proof marks."
1400s-1500s
Full Plate
Armor got pretty serious. Towards the end of the full-plate armor times, the shield was generally not used, as the thickness of the breastplate grew.
German Armor, 1548
www.metmuseum.org
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OK, so do I think a .410 shotgun at 5' would penetrate armor made in the 1500s?
Maybe.
It would depend on:
1. Shot type. Slug increases chance, birshot decreases chance.
2. Angle of incidence. A shot to the breatplate for two squared-off opponents means that the angle of incidence is NOT 90deg, due to armor design
3. Location of hit. Hits to the breastplate decrease liklihood of penetration. Hits to extremities increase liklihood.
The later the armor, the less the likilihood of the .410 penetrating, with Napoleaonic-era breastplates being toughest to penetrate. What is .410 birdshot or even a slug compared to a musket ball fired from one of Wellington's men?
Of course, I am not willing to prove it by donning such armor and catching .410 shot/slugs. Empiricism is all fine & dandy, until its my chestnuts in the fire.
Slugs would penetrate probably out to 150-200 yards. A .410 slug weighs in at about 140grains IIRC, and runs about 1300-1500fps. A 9mm is about 115-147gr going about 1300-1000fps for given weights. I would prefer a .410. 
